Honestly, I don't remember any actual military stuff used in StarTrek, really. You right about uniforms and military-like teams, but all their weapons and military stuff was SciFi props, not some DoD stuff. IDK, may be it was in some episode about time travel into our time, but that's only one episode that have to be vetted by DoD to allow using DoD stuff, not whole series.
As for crews in uniforms, civilian ships and planes often have uniformed crews too.
Stargate - yes, they used actual military equipment heavily in their series.
And it is Stargate series SG-1 that fit your theory fully without any contadictions, including predictive programming, cover-ups, and propaganda. They even had self-satire episode about fictional TV series show used as cover-up for TV series heroes stargate program. :)
Honestly, I don't remember any actual military stuff used in StarTrek, really. You right about uniforms and military-like teams, but all their weapons and military stuff was SciFi props, not some DoD stuff. IDK, may be it was in some episode about time travel into our time, but that's only one episode that have to be vetted by DoD to allow using DoD stuff, not whole series.
As for crews in uniforms, civilian ships and planes often have uniformed crews too.
Stargate - yes, they used actual military equipment heavily in their series.
And it is Stargate series SG-1 that fit your theory fully without any contadictions, including predictive programming, cover-ups, and propaganda. They even had self-satire episode about fictional TV series show used as cover-up for TV series heroes stargate program. :)